We propose to develop and analyze a set of mathematical models aimed at understanding the humoral immune response and the generation of immune memory. In vivo, immune responses occur primarily in secondary lymphoid organs. Germinal center formation and somatic hypermutation of antibodies being critical aspects. The regulation and control of these local events are currently under intense experimental scrutiny and involve an interesting set of quantitative problems related to B and T cell population dynamics, control of somatic mutation, the selection events driving affinity maturation, the generation of immune memory, and the role of the spatial structure and local germinal center environment in these processes. Theoretical and quantitative analysis of these issues may be able to generate new ideas and insights. Our models will address the events occurring during B cell responses in splenic foci and germinal centers, concentrating on antigen retention by follicular dendritic cells, somatic mutation and the role of the spatial structure of germinal centers in selecting high affinity cells. We also propose to develop physical chemical theories for affinity based selection, and will examine the role of somatic mutation in the immune response to evolving pathogens. Specific health related issues include improving our understanding of the generation of immune memory and hence our ability to make more effective vaccines, and hate role of somatic mutation in providing protection against rapidly mutating pathogens. Further, progress in developing comprehensive quantitative models of immune system events will improve our understanding of the operation of the immune system as a whole in fighting disease.